The time required to reach a windward mark on a passage of a sailing yacht is dependent upon the Velocity Made Good (VMG) which, among other things, is greatly influenced by four major factors: the amount of leeward drift of the vessel, the heeling angle of the vessel, the effective weight of the vessel, and the drag on the vessel.
Velocity Made Good (VMG) is defined as that component of a sailing vessel's velocity made good toward windward. It is that component of a vessel's velocity which is directly opposite to the direction of the true wind.
The aerodynamic and hydrodynamic fluid forces that act on a sailing vessel as it moves toward its windward mark or destination can be resolved into components that are parallel and perpendicular to the direction of undisturbed fluid flow. The component parallel to the direction of undisturbed fluid flow is called a driving force when acting in a forward direction or drag when opposing forward motion. The component perpendicular to the direction of undisturbed fluid flow is called lift. The lift force of the sails is perpendicular to the direction of the apparent wind and lift force of the hull is in a plane perpendicular to the course sailed (PPCS).
The leeward drift of a conventional keeled sailing vessel is a result of the lateral component of the wind force on the exposed surface area above the waterline (including sails, rigging, and hull) and the lateral component of the water forces acting on the surfaces below the waterline, including the hull, keel, and rudder. In order for a vessel to sail toward its windward mark, the keel and rudder must provide resistance to the leeward drift forces. Since a conventional keel is symmetrical, this can only be accomplished by establishing a leeward angle of attack which makes the vessel angle, or crab, toward its objective. The leeward angle λ is defined as the angle between the course steered and the course, or track, sailed.
The minimum resistance offered by the water to forward motion of the canoe body and keel of a sailing vessel occurs when the vessel is pointed directly opposite to the incident fluid flow, that is, in the direction of the course sailed. Therefore, directing a vessel at a leeward angle to its track through the water increases the drag on its hull and keel. The increased drag reduces the forward velocity of the vessel. The decrease in the forward velocity, in turn, reduces the velocity made good, VMG.
The heeling angle of a sailing vessel is proportional to the lateral forces of the wind pressing upon its sails, rigging and hull as well as lateral water forces on its hull, keel and rudder. When a vessel is sailing upright, or perpendicular to the plane of the surface of the water, it captures the maximum available wind and therefore has the maximum amount of wind energy to convert into forward propelling energy. When a sailing vessel is heeling, the horizontal projection of the sail area is reduced in proportion to the increase in heeling angle. Thus, forward propelling energy is lost because less wind energy is captured by the sails. Unfortunately, what suffers most when the sails are inclined is the production of the upper areas of the sails since they are brought closer to the water surface where, due to wind shear, the wind velocity is lower. It is not uncommon for the wind velocity at deck altitude to be 25% less than velocity at the top of a 45 foot mast. Since the wind force is proportional to the square of the velocity, this translates to about a 43% reduction in wind force. Therefore, as a boat heels, the sails are withdrawn from the location where the wind force is significantly greater.
The aerodynamic and hydrodynamic forces that act on a sailing vessel can be considered to be perpendicular to the surfaces that generate them. When a vessel is sailing erect, therefore, the total sail forces are most effective because they are directed within the horizontal plane of travel. However, when a vessel heels, the total sail force is no longer directed in the horizontal plane of travel but is angled down by a degree equal to the heeling angle. Thus, the forward propelling force—that component of the total sail force that is parallel to the incident water flow and thus acts to drive a sailing vessel in the direction of travel—is also reduced.
The heeling angle also creates a vertical component of the wind force that, like gravitational weight such as ballast, acts in a downward direction. This downward component of the force is lost to forward propelling energy and without compensation would also contribute to the effective weight of the vessel and thereby increase the displacement, wetted surface, and associated drag. The lift force generated by the symmetrical keel of a conventional sailing vessel is in a plane perpendicular to the course sailed, PPCS, and is a function of the angle of attack of the keel to the incident water. Therefore when the helm compensates for an increased leeward drift force by increasing the leeward angle, the angle of attack of the keel is increased. The increased lift force so produced comprises a horizontal component that counters the leeward drift force of the sails and an upward vertical force component that counters the downward force exerted by the sails, thus returning the vessel to equilibrium and maintaining its original track. This is not without cost, however, because the higher angle of attack increases the induced drag on the vessel.
Other losses are introduced by heeling because the shape of the hull is usually optimized for minimum drag and/or wetted surface when the vessel is sailing upright or perpendicular to the plane of the water. For this reason, the drag is also increased by heeling, at an additional expense to the forward velocity of the vessel.
Further, the horizontal force that the keel provides to resist leeward drift is a function of the heeling angle of a vessel and, all other things being equal, is diminished as the cosine of the heeling angle diminishes with an increase in the heeling angle.
The weight, or more properly, the effective weight of a sailing vessel, at any given moment, determines the displacement and therefore the wetted surface and related drag on a sailing vessel. A decrease in the effective weight results in a decrease in the wetted surface and associated drag with an attendant increase in forward velocity. Less effective weight also improves the vessel's ability to reach a planing condition.
As stated above, a decrease in weight or effective weight is accompanied by a decrease in drag on a sailing vessel. A decrease in the effective weight can be achieved by a reduction in the heeling angle which will redirect the force exerted by the sails into a more horizontal direction. Accordingly, cascading benefits will accrue: a proportional component of the sail force will be converted from a vertically downward or effective weight force into forward driving force which increases the velocity of the vessel; a higher velocity permits a reduction in the leeward angle that must be sailed in order to reach a given mark; the reduced leeward angle decreases the drag associated with the angle of attack of the keel and the crabbing of the canoe body of the sailing vessel.
The overall efficiency of a sailing vessel can be substantially improved by a decrease in leeward drift, heeling angle, effective weight, or drag; provided, of course, that the improvement in any one of these characteristics is not obtained at an equivalent or greater expense of one or more of the other characteristics.
Early yacht designs incorporated fixed, symmetrical appendages known as conventional keels, which extended down from the hull in alignment with the vertical longitudinal midplane of the vessel. An essential function of the keel was to resist leeward drift caused by the lateral component of wind force on the vessel. This required a vessel to maintain a heading at a leeway angle to the course sailed.
Later designs for sailing vessels have utilized asymmetric hydrofoils intended to counter the forces that cause leeward drift. Although efficient in this regard, the horizontal and vertical components of the forces exerted by these hydrofoils, however, either increased the heeling force, or increased the effective weight.
U.S. Pat. No. 6,032,603 discloses such a prior art, asymmetric hydrofoil, keel design. FIG. 3 of that patent is reproduced as FIG. 1 here. The sailing vessel is shown on a starboard tack heeling at an angle of 20 degrees. The hydrofoil is mounted on the keel, with its cambered surface facing toward the windward side, to create a generally windward directed, counter-leeward drift force. This does give relief to the leeward drift forces acting on the vessel; that is, the counter leeward-drift force equals the lateral force, Q, generated by the hydrofoil, times the cosine of the heeling angle of the vessel. The hydrofoil also generates, however, a heeling moment which is equal to the force, Q, times its perpendicular distance from the line of that force to the (instant) axis of rotation of the sailing vessel.
Symmetric keels of traditional sailing vessels oppose leeward drift by sailing at a leeward angle to the track of a vessel but leeward drift can also be opposed by an asymmetric hydrofoil designed and located to provide counter-leeward drift forces. The latter is more efficient in two ways. First, for a given value of counter-leeward drift force, an asymmetric hydrofoil can move at a lower angle of attack thereby inducing less drag; and second, since the counter-leeward drift force generated by an asymmetric hydrofoil reduces the required leeward angle, it permits the vessel to point closer to its desired track. It is noteworthy that although an asymmetric hydrofoil does not require sailing at a leeward angle to produce a counter leeward drift force as does a symmetric keel shape, if necessary it can do so, which would increase its angle of attack and thus its lifting force and, like its symmetric cousin, but to a lesser extent, its drag will also increase.
FIG. 1 provides an example of an asymmetric hydrofoil mounted on the keel of a sailing vessel. The hydrofoil has a cambered surface facing generally toward the windward side of the vessel and a non cambered surface facing generally toward the leeward side of the vessel. The velocity over the cambered surface is higher than the velocity over the non-cambered surface and according to Bernoulli's principal, an increase in velocity will be accompanied by a proportional decrease in pressure. Thus, in this case, differential between the lower pressure on the cambered side and the higher pressure on the non-cambered side of the hydrofoil produces a force Q toward the windward side of the vessel. Then, as shown, its horizontal component serves to oppose leeward drift forces acting on the vessel. It must be noted though, that force Q also acts at a perpendicular distance from the instant axis of rotation of the vessel and force Q multiplied by this distance exerts a heeling moment that adds to the existing heeling moments acting on the vessel.
When the wind presses upon the sails of a traditional sailing vessel, the vessel heels and the center of buoyancy moves from the midplane of the vessel to leeward. Since the weight and buoyancy forces are then no longer in vertical alignment, they form a counter-heeling couple, tending to right the vessel. When additional counter-heeling moments were required, designs called for additional weight or ballast to be added to the lower end or tip of the keel. Therefore, when a vessel heeled, the ballast acted on the moment arm, so provided, to exert an additional moment to counter the heeling moments leveraged by the wind on the vessel. The amount of ballast that is required to provide an adequate amount of counter-heeling moment can add significantly to the weight of the vessel. Still, such conventional designs afford only limited control of the righting moment and the heeling angle can only be further reduced by lateral motion of the crew or on-board moveable weight.
More recently, a canting keel has been introduced to provide a counter-heeling moment by suspending a ballast bulb beneath the hull on a laterally swinging or canting member that increases the anti-heeling lever arm of the ballast when rotated toward the windward side of a tacking sailing vessel. Such mechanisms do resist heeling moments but, like conventional ballast, because they function gravitationally, considerable weight must be incorporated in their design. Additionally, a keel canted to a severe angle can do little to resist leeward drift forces. Therefore, supplementary fore and aft appendages must be added to provide the necessary counter-leeward drift forces.
A subsequent development in the canting keel is the addition of a hinged hydrofoil or flap mounted on a canting keel or strut that connects the hull to the ballast. This hydrofoil, or flap, is intended to provide additional heeling resistance when it is necessary to increase the anti-heeling force because the ballast has been canted to its limit and operating conditions require additional anti-heeling force.
U.S. Pat. No. 5,622,130 discloses such a flap. FIG. 1 of that patent is reproduced as FIG. 2 here. As can be seen, the counter-heeling flap or hydrofoil 20 is mounted on the trailing edge of the keel or strut 14 on an axis along, or parallel to, the longitudinal dimension of the strut 14. When activated, unless the keel 14 is vertical, the force generated by the hydrofoil 20 will be at an angle to the horizontal. Since the flap would only be activated when the vessel was heeling, its hydrodynamic force would be at an angle to the horizontal. Therefore, as that force acts to resist heeling, it has components that exert both a horizontal force that increases the leeward drift of the vessel and a downward force that adds to the effective weight of the vessel. Compensation for the increase in these forces can be made by increasing the leeward angle and thus the angle of attack of the keel.
An example makes this clear. FIG. 3 is a stern view schematic of the prior art shown in FIG. 2 with the appendages 16 and 18 omitted for clarity. As shown in FIG. 3, the flap 20, mounted on a canting keel 14 of a sailing vessel, is at an angle of 42 degrees to the vertical because the vessel is heeling at an angle (Phi) of 20 degrees, with its keel canted at an angle (Kappa) of 22 degrees from the midplane of the vessel. When flap 20 is actuated to exert an additional counter-heeling force (FCH), the horizontal, or drift component of this force (FD), would equal FCH×cosine 42 degrees, or 0.743 FCH acting in a leeward direction, thus increasing the drift of the vessel. The vertical or weight component of force FCH, called FW, would equal FCH×sine 42 degrees, or 0.669 FCH acting in a downward direction, increasing the effective weight of the vessel.
Other early designs offer embodiments that were intended to counter the leeward drift forces and the heeling moments with appendages or foils that function hydrodynamically. Such foils, however, produce components that exert significant downward forces on the sailing vessel. These forces mimic the weight disadvantage of ballast, and tend to pin down or pull the vessel deeper into the water, increasing the displacement, the wetted surface, and the attendant drag, all of which tax the velocity of the vessel. In addition, depending upon the attitude, shape or efficiency of the hydrofoil, these forces may create significant additional heeling moments proportional to the amount of leeway that the vessel is making.
Australian Patent Application AU-A-85 668/82 exemplifies such a design. The embodiment shown in FIG. 3 of that patent is shown here as prior art FIG. 4. As seen in FIG. 4, the vessel is shown heeled 20 degrees on a starboard tack. Two fins, 5a and 5b, which are shaped and positioned to produce hydrodynamic forces in a generally downward direction, are shown. The fins are fixed to the tip of the keel and the surfaces on their undersides are angled at 20 degrees down from the horizontal when the keel is in the vertical position. According to FIG. 4, the force Q′ on the windward side, named herein Q′W, is equal to the force Q′ on the leeward side, named herein Q′L. If so, the windward fin 5b produces no counter-leeward drift lift while the leeward fin 5a produces a counter-leeward drift equal to Q′L Sin 40° for a net decrease in the leeward drift forces acting on the vessel. An additional advantage is obtained because the angle of the fins increases the effective span or draught of the keel as the vessel heels. However, FIG. 4 also shows that the vessel must bear the vertically downward or effective weight forces exerted by both hydrofoils. Together, these downward or effective weight forces are the sum of the vertical components of the forces exerted by the hydrofoils, that is: Q′W plus Q′L Cos 40°=1.766 Q′.
Still, other prior art keel designs that generate counter-heeling moments either have no compensation on the keel for the drift forces that are necessarily introduced by such counter-heeling designs, or additional appendages are added elsewhere on the hull to counter the drift forces. If such compensation is provided by a single counter-leeward drift appendage, not in line with the keel, it will likely establish a yawing moment that can reduce the efficiency of the vessel and compromise the rudder's ability to control the vessel. Two such appendages working to compensate for said counter-heeling device could be added to the hull to provide counter-leeway drift forces and yawing control but likely would add complexity to the system and drag to the vessel.
The above-mentioned considerations associated with keels, canting keels, associated hydrofoils and the like apply to the design of any class of sailing vessel. The need exists for an improved design that reduces heeling, leeward drift, weight, and drag in such a manner that an improvement in one does not significantly degrade another.
This need is particularly acute in the design of high performance sailing yachts specifically designed for the America's Cup Race. Improved designs for America's Cup Class Yachts must conform to the specifications required by the America's Cup Class Rule Version 5.0
In consideration of designs disclosed herein that are intended to qualify for America's Cup Class Rule Version 5.0, three requirements, which have related significance, are noted. First, Rule 17.10 states: “The maximum number of movable appendages shall be two . . . ” Second, Rule 17.10(a) further limits the movement of these appendages “to rotation only.” Third, The Deed of Gift, written in 1887, that established America's Cup Races, contained a few select rules that must be followed to this day, including the following: “Center-board or sliding keel vessels shall always be allowed to compete in any race for this Cup, and no restrictions nor limitations whatever shall be placed upon the use of such center-board or sliding keel, nor shall the center-board or sliding keel be considered a part of the vessel for any purposes of measurement.”
Four formulae of America's Cup Class (ACC) Rule, Version 5.0 that govern the design requirements for sailing vessels competing in The America's Cup are of particular importance. These formulae place interacting restrictions on the variables: Rated Length in meters (L), Measured Length in meters (LM), Displacement in cubic meters (DSP), Rated Sail Area in square meters (S), a Weight Penalty, by definition in meters (WP), Weight in kilograms (W), and a Freeboard Penalty in meters (FP).
They are bound in the primary formula of Section B, 5:[L+1.25×(S)−2−9.8×(DSP)−3]/0.686<=24.000 metres  (a)and defining formulae, respectively, of Section B, 6.1; Section B, 8.1 and Section C, 12.2:L=LM×[1+2,000×(LM−22.1)4]+FP+WP,  (b)DSP=W/1025, where 1,025 kgs/m3 is the density of sea water  (c)WP=4×[(yacht's weight in kgs)−3−28.845]  (d)Formula (a) shows that the factors L and/or S can be increased when DSP, which is equivalent to weight, increases. However, formula (d) shows that for any vessel exceeding 24,000 kilograms a weight penalty (WP) is imposed and according to formula (b) the weight penalty WP will dictate either a reduction in the measured length LM or an increase in the value of the rated length L. Referring back to formula (a), if L is increased, S must then be reduced to maintain the formula limit of 24 meters. It might be noted that an increase in the weight W also increases displacement DSP but this does little to counteract the disadvantage imposed by the weight penalty WP.
The effect of how a weight change manifests itself on the relative values of L and DSP in formula (a) can be shown in the following example, wherein the weight of a vessel W=27,000 kilograms:
It is evident from formula (b) that any change in WP is comparable to a change in L. Also, to be on an equal footing in formula (a), a change in L, hence WP, must be compared to a change in the factor “9.8(DSP)−3”. When the weight of the vessel changes, as in this example, from 24,000 kgs to 27,000 kgs, the components WP and Δ9.8(DSP)−3 compare as follows:
                                                        WP              =                            ⁢                              4                ⁡                                  [                                                                                    (                                                  27                          ,                          000                                                )                                                                    -                        3                                                              -                                                                  (                                                  24                          ,                          000                                                )                                                                    -                        3                                                                              ]                                                                                                        =                            ⁢                              4                ⁡                                  [                                      30                    -                    28.845                                    ]                                                                                                        =                            ⁢                              4.62                ⁢                                                                  ⁢                                  meters                  .                                                                                1                                                                              Δ                ⁢                                                                  ⁢                9.8                ⁢                                                      (                    DSP                    )                                                        -                    3                                                              =                            ⁢                                                9.8                  ⁢                                                            (                                              27                        ,                                                  000                          /                          1025                                                                    )                                                              -                      3                                                                      -                                  9.8                  ⁢                                                            (                                              24                        ,                                                  000                          /                          1025                                                                    )                                                              -                      3                                                                                                                                              =                            ⁢                              9.8                ⁢                                  (                                      2.97                    -                    2.86                                    )                                                                                                        =                            ⁢                              1.08                ⁢                                                                  ⁢                                  meters                  .                                                                                2                                                                              WP                -                                  Δ                  ⁢                                                                          ⁢                  9.8                  ⁢                                                            (                      DSP                      )                                                              -                      3                                                                                  =                            ⁢                              4.62                -                1.08                                                                                        =                            ⁢                              3.54                ⁢                                                                  ⁢                meters                ⁢                                                                  ⁢                                                      (                                          11.6                      ⁢                                                                                                                        ⁢                                                                                                                      ⁢                      feet                                        )                                    .                                                                                3      
Therefore, assuming that the Freeboard Penalty (FP) remains unchanged, the Measured Length LM would have to be decreased sufficient to reduce the value of rated length L by 3.54 meters in order to compensate for the Weight Penalty WP in this example.
It can be seen that, all other things being the same, for a vessel of a given rated length L and weighing more than 24,000 kg, a decrease in the weight, and therefore a decrease in the weight penalty, (WP), will allow an increase in the measured length (LM) and thus an increase the maximum attainable velocity of such a high performance racing yacht. An alternative would be to not change LM, which would then reduce the value of the rated Length L. This would then permit an increase in the sail area. Therefore, it is desirable to enable designers of sailing vessels in this category to increase counter-heeling moments without adding additional ballast and without suffering additional drift forces.
Accordingly, the present invention is directed toward overcoming the aforementioned problems associated with keel arrangements and designs, thus creating a more efficient sailing vessel in any class or category. The present invention is further directed toward improved designs, embodiments, and systems that enable the improvement of any one, or any combination, of the above cited performance characteristics. The present invention is still further directed to overcoming the aforementioned problems associated with keel arrangements and designs while adhering to the design rules required for boats to participate in the America's Cup Race.